Solve for $x$ and $y$ using elimination. ${5x-y = 49}$ ${-6x+y = -59}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-x = -10$ $\dfrac{-x}{{-1}} = \dfrac{-10}{{-1}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {5x-y = 49}\thinspace$ to find $y$ ${5}{(10)}{ - y = 49}$ $50-y = 49$ $50{-50} - y = 49{-50}$ $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ You can also plug ${x = 10}$ into $\thinspace {-6x+y = -59}\thinspace$ and get the same answer for $y$ : ${-6}{(10)}{ + y = -59}$ ${y = 1}$